How to make a cross tee pipe fitting in Blender?
Final:

I do know that you said you don't want to use Subdivision Surface modifier, but just check those numbers:



Steps:




Select four faces around a Cube.
In Tools Panel choose Extrude Individual and enter desired number or move your mouse (I've entered '1').
Delete selected faces.
Add Subdivision Surface modifier.
(Optional) Add Solidify modifier.
(Optional) In Data tab check AutoSmooth and set Angle to 60 degrees.